1 / 27

Decision analysis

Decision analysis. Rationality. Uncertainty. 서울대학교 공과대학 산업공학과 신 준 석. What beneath our decision. The root of failure Why decision analysis? What we should do when we do not know what to do Intuition  Experience & Program  Analysis. Discrepancy. Uncertainty. Past decisions. Decision.

hollye
Download Presentation

Decision analysis

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Decision analysis Rationality Uncertainty 서울대학교 공과대학 산업공학과 신 준 석

  2. What beneath our decision • The root of failure • Why decision analysis? • What we should do when we do not know what to do • Intuition  Experience & Program  Analysis Discrepancy Uncertainty Past decisions Decision Irrationality

  3. Type of usual decision • Three general types • What we usually do could be divided into 3 types Intuitive Simple & easy work Time pressure works Individual attitude-dependent Routinized work Deterministic events Usually rule-based Programmed Analytical Complex work Highly uncertain events & Various alternatives Statistics-based & data-dependent

  4. Decision model • Why model? • - Need to express the real world quantitatively and logically • Components • Probability: An estimate of all uncertainty-related information • Relationship: among variables included in the model • Alternative: What we actually choose Alternative Decision model Probability Real world Relationship

  5. Type of decision: revisited • Newly defined types • Decision model defines 3 types of decision Decision Under certainty Obvious alternatives Deterministic events Predictable results No or little prior knowledge Uncertainty dominates Probability induced Decision Under uncertainty Decision Under risk Obvious alternatives Well-defined events Probability induced

  6. Alt. S1 S2 S3 S4 Res. 6,000 3,000 4,000 5,000 ? Decision under certainty • When could we do? How to? • Pre-condition • Controllability: All ‘key’ variables should be controllable • Deterministic events : Absolute one-to-one correspondence between an alternative and a result • The process Identify variables Arrange alternatives Calculate results Comparison

  7. Decision under uncertainty • When could we do? How to? • Pre-condition • No predictability or predictable but doubtful • Methods • Pessimist : A premise based on the occurrence of the worst event • Wald criterion (Mini-max, Maxi-min) • Savage criterion • Optimist : A premise based on the occurrence of the best event - Mini-min, Maxi-max • Neutralist: neither pessimistic nor optimistic - Laplace-Bayes, Hurwicz

  8. Pessimist’s case • Wald criterion • Mini-max • Calculate all minimum-values • Choose an alternative which has maximum among them (A2!) • Maxi-min • Calculate all maximum-values • Choose an alternative which has minimum among them (A2? A3?)

  9. Pessimist’s case • Savage criterion • Concept: Minimize the opportunity cost • Process • Calculate all opportunity cost • Choose an alternative which has minimum among them (A1!)

  10. Optimist’s case • Maxi-max or Mini-min • Concept: Maximize the profit and minimize the cost • Process • Calculate all maximum (minimum) values • Choose an alternative which has maximum (minimum) among them (A3 in both cases)

  11. Neutral: neither pessimistic nor optimistic • Laplace-Bayes criterion • Concept • Premise: An uniform distribution of events • Process • Calculate expected values • Choose an alternative which has the maximum expected value (A1!)

  12. Neutral: neither pessimistic nor optimistic • Hurwicz criterion • Concept • Combination of a pessimistic view and an optimistic view • Process • Using a coefficient α: 0(pessimistic)<=α<=1(optimistic) • Calculate αMax(Ai)+(1-α)Min(Ai) • According to the pre-determined α, choose the alternative In the case of α=0.15, choose A2!

  13. Decision under risk • When could we do? How to? • Pre-condition • Predictability : Key variables could not be controlled but be predicted • Probabilistic events : An alternative corresponds to a distribution of results • The methods • Dominance - Probabilistic dominance, outcome dominance • Mean-variance • Same mean, smaller variance • Larger mean, same variance • Certainty equivalent • Expected value

  14. Dominance • Outcome dominance • Concept • One alternative is better than the other alternative in all cases • In all cases of Vi, A1>=A2, in more than one case, A1>A2 • The process • One-to-one comparison in all cases • Check the 1st condition A1>=A2 in all cases • Check the 2nd condition A1>A2 in more than one case A1 dominates A2, A1 can’t A3, then A2 & A3?

  15. Dominance • Probability dominance • Concept • The probability A1>=A2 is greater than that of A1<A2 • The process • Calculate the cumulative probability function F1(V), F(V) • Check the condition F(x)>=F(y) over the whole Vi Alternative 1 Cumulative probability Alternative 2 Result(output)

  16. Mean-Variance • Mean-variance dominance • Concept • The larger the mean, the better the alternative is • The smaller the variance, the better the alternative is • The process • If the one factor is same, compare the other factor • If not, use the mean-variance ratio A1 dominates A2, then A1 & A3?

  17. Certainty equivalent • CE: certainty equivalent • Concept • The larger the CE, the better the alternative is • The process • Judge the value of CE • The larger the CE is, the better the alternative is Alternative 1 Alternative 2 5,000 0.5 5,000 0.4 CE=1,500 CE=1,800 0.5 0 0.5 1,000 A2 dominates A1

  18. Decision tree • Where to use? • Definition: Expected-value based decision model • Which problem? • Multi-stage decision making • Monetary aggregates measurement • Symbols • Decision node • The point where the decision made • Graphical representation: • Event node • The point where the event branches off • Graphical representation:

  19. Decision tree • Reception problem (Howard, 1984) • Problem • Decision – the place? Outdoor? Indoor? Half-way? • Event – the weather? Fine? Rainy? • The modeling process • Arrange the alternatives 3 alternatives: Outdoor, Indoor, Half-way • Identify the key variable with regard to uncertainty A key variable: weather The variable state: Fine or rainy • Predict the output fixing the alternative & event • Express the output as a monetary unit

  20. Decision tree • Graphical representation Fine Outdoor Excellent 1,000 Rainy 0 Catastrophe Fine Half-way 900 Success Rainy Failure 200 Fine Indoor 400 Slight failure Rainy Slight success 500 Monetary unit!!!

  21. Decision tree • Decision based on expected value 0.4 Fine Outdoor Excellent 1,000 Rainy 0 Catastrophe 0.6 0.4 Fine Half-way 900 Success Rainy Failure 200 0.6 0.4 Fine Indoor 400 Slight failure Rainy Slight success 500 0.6 • Expected value comparison • Outdoor EV=0.4*1,000+0.6*0=400 • Half-way EV=0.4*900+0.6*200=480 • Indoor EV=0.4*400+0.6*500=460

  22. A problem • What beneath EV • Question • Is the value always same? • Where is the uncertainty & risk? • Where is the attitude of the decision-maker? • What we should do • Bring the risk & uncertainty into the model • Bring the individual attitude on the value into the model • St. Petersburg paradox • A coin game • The rule • : N trial, Heads: Win 1000*2n Tails: Lose • EV=(1/2)*2000+(1/2)2*4000+….= infinite • Question: Do you join this game?

  23. Utility function introduced • Utility function • Utility • Different from the ‘satisfaction’ concept of economists • Degree of preference over risky alternatives • Utility curve • : the graphical representation of the relation between utility and the other value such as revenue, cost and so on Utility Utility Utility Revenue Cost Inventory

  24. Utility function • Utility function • Fix the unit & range • Monetary unit: ~Won. • Monetary unit range: 1~1000 • Match the utility value with monetary value • Graphical representation of the relationship U(x) Utility Monetary unit

  25. Decision tree • Decision based on utility 0.4 Fine Outdoor Excellent 1,000 1 Rainy 0 0 Catastrophe 0.6 0.4 Fine Half-way 900 0.951 Success Rainy Failure 200 0.323 0.6 0.4 Fine Indoor 400 0.569 Slight failure Rainy Slight success 500 0.667 0.6 • Utility comparison • Outdoor EV=0.4*1+0.6*0=0.4 • Half-way EV=0.4*0.951+0.6*0.323=0.574 • Indoor EV=0.4*0.569+0.6*0.667=0.628

  26. Information • Use or not? • Why? • Decrease the uncertainty • Hesitate or reject? • Wrong information  A big loss • The cost that we should pay  Benefit > cost? • How to use? • Perfect information • EVPI (expected value of perfect information) = EV using information – EV ignoring information • Imperfect information • EVSI (expected value of sample information) = EV using sample information – EV ignoring sample information

  27. Perfect information case • Perfect information about the ‘weather’ Outdoor 1,000 Information ‘fine’/ 0.4 Half-way 900 Indoor 400 Outdoor 0 Half-way 200 Information ‘rainy’/ 0.6 Indoor 500 • EVPI? • EV of this tree=0.4*1000+0.6*500=700 • EV of the previous tree=480 • EVPI = 700-480=220  the value of information

More Related